Including an unfavourable destabilizing effect due to an iron-core transformer, the positional instabilities were investigated for a horizontal expansion and vertical displacement of the tokamak plasma loop. The strong interaction of a current-carrying plasma loop with an image field as a result of the iron-core magnetization produces a considerable attractive force on the plasma loop towards the iron core. It is shown that the stability condition has a large dependence on the equilibrium position of the toroidal plasma and such parameters as the kinetic pressure of the plasma. It is also pointed out that the destabilizing effect due to an iron core restricts the stability margin against positional instabilities within narrow limits in most of the iron-cored tokamaks.